1) Many children are proud of their father. (Should it be father or fathers?) You could say either here." father" singular sounds slightly more natural to me. In this case, because children tend to only have one father. 2) The education level female received has increased dramatically. (Should it be female or females?) "Females" is correct. and it should be "receive" (present tense). 3) In the past, women need to take care of their children, clean the house and cook the meal. (Is "the" here necessary, and do I need to write "houses" and "meals" instead of their singular forms?) "In the past" is a standard phrase, you can't say "In past". Also, you're talking about the past, so you need to use the past tense i.e. "needed". You could say "look after their houses" but often in plural cases like these, you take the plural "women" to refer to the group as a whole. Then when you expand on it, imagine you are speaking about one woman in particular (this is the case with the earlier examples too). Therefore, "house" is singular". However, "meals" should be plural, but that is for a different reason. "meals" should be plural because you have more than one meal a day. So it's like saying "they needed to prepare all the meals for the day".

1) It should be father. While many children may have different fathers, each child can have only one (biological) father. 2) In this context, it should be females as you're talking about more than one. Received should also be "receive". 3) Need -> needed, house should be singular as most families only own one house, meal should be meals because a family is going to eat multiple meals.